The log-convexity of the fubini numbers

Let $f_n$ denotes the $n$th Fubini number. In this paper, first we give upper and lower bounds for the Fubini numbers $f_n$. Then the log-convexity of the Fubini numbers has been obtained. Furthermore we also give the monotonicity of the sequence $\{\sqrt[n]{f_n}\}_{n\ge 1}$ by using the aforementioned bounds.